PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Identifying Elementary Iterated Systems through Algorithmic Inference: the Cantor Set Example
bruno apolloni and simone bassis
Chaos, Solitons and Fractals Volume 30, pp. 19-29, 2006.

Abstract

We come back to the old problem of fractal identification within the new framework of Algorithmic Inference. The key points are: i) to identify sufficient statistics to be put in connection with the unknown values of the fractal parameters, and ii) to manage the timing of the iterated process through spatial statistics. We fill these tasks successfully with the Cantor Sets. We are able to compute confidence intervals for both the scaling parameter $\vartheta$ and the iteration number $n$ at which we are observing a set. We both check ùly the coverage of these intervals and delineate a general strategy for affording more complex iterated systems.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:4463
Deposited By:Bruno Apolloni
Deposited On:13 March 2009